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Tumor growth modeling via Fokker–Planck equation

Author

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  • Heidari, Hossein
  • Karamati, Mahdi Rezaei
  • Motavalli, Hossein

Abstract

In the present investigation, a stochastic tumor growth model is presented based on the Morse potential. The solution of the Fokker–Planck equation is used to study the growth rate and the geometry of breast cancer with and without radiation therapy effects. In the second case, to estimate unknown parameters of the probability density function, breast data from the Surveillance, Epidemiology, and End Results program and machine learning algorithm are used. By considering three groups of women (35–85 years old), the results show that as time goes on, tumor size increases while its growth rate decreases, and the older women have a slower growth rate. Also, the simulation results of breast tumors of mice confirm that our results are consistent with the experimental evidence in both cases of radiotherapy and no treatment. Finally, the finding of this study implies that the present model is accurate than the Gompertz one in predicting tumor size, in the treatment case.

Suggested Citation

  • Heidari, Hossein & Karamati, Mahdi Rezaei & Motavalli, Hossein, 2022. "Tumor growth modeling via Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    • Handle: RePEc:eee:phsmap:v:596:y:2022:i:c:s0378437122001753
    DOI: 10.1016/j.physa.2022.127168
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    References listed on IDEAS

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    1. Borges, G.R.P. & Filho, Elso Drigo & Ricotta, R.M., 2010. "Variational supersymmetric approach to evaluate Fokker–Planck probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3892-3899.
    2. Aleksey S. Polunchenko & Grigory Sokolov, 2016. "An Analytic Expression for the Distribution of the Generalized Shiryaev–Roberts Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1153-1195, December.
    3. Lo, C.F., 2019. "Exact solution of the functional Fokker–Planck equation for cell growth with asymmetric cell division," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
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